A couple of points. Firstly, I think that there are problems with the original line shapefile. These can be put right using GRASS v.clean using the "snap" option. Try with a threshold of 5 to start with, but just 1 might do. GRASS v.clean can be run from the Sextante toolbox (it's very easy to use).

Secondly, for polygonising I should try the excellent "Polygonizer" plug-in. This needs the Shapely (python-shapely) package to be installed, which can be done using the OSGeo4W Installer or in Ubuntu using the package manager.